They're the good and bad paths respectively. Coincidentally, they're also the outcomes of pushing Sho when he asks you to stop. (Spoilers for the routes ahead, obviously.)
To get the A path, be firm and push all the way through. You have to knock some sense into Shoichi, so you have to never stop pushing him. Talk back to his dad, be firm, and keep pushing him to go visit his mom.
To get the C path, you're gonna have to have a change of opinions, which will make Shoichi mad. You can either choose to not talk back to his dad or be apologetic. After choosing any of those two and then pushing him to visit his mom, it will set you up to the C path.
You know you got the A path if he agrees to visit his mom. You know you got the C path if he doesnt talk to you for a few days.